The article concerns problems related to the assessment of reactive power in power networks with non-linear, fast-varying loads, such as electric arc furnaces, rolling mill drives, etc. The operation of this type of loads is characterized by the introduction of interharmonic currents (including higher harmonics) into the power supply network and a relatively low power factor. Rapid changes in the RMS value of the current also cause voltage fluctuations and the related phenomenon - flicker. Therefore, there is a need to evaluate the selection of power of compensating devices taking into account the random nature of load changes and the distortion of current and voltage waveforms, in particular interharmonic components, the impact of which has not been fully investigated so far. To analyze the random nature of load changes, autocorrelation functions were used, which allowed for the estimation of the expected values of the arc furnace current distortion coefficient (based on the recorded waveforms). In order to determine the parameters of reactive power compensating devices, and in particular capacitor banks, an autocorrelation function in the exponential-cosine-sine form was used, which meets the conditions of differentiation. The article contains comparative results of calculations of the reactive power of capacitor banks determined using different methods.

The calculation of power flow in power systems with the presence of harmonics has been properly studied in the scientific literature. However, power flow calculation considering interharmonic components is still an open question. Traditional methods based on the IEEE1459 standard have proven to be valid and accurate only for linear and sinusoidal systems, but have been criticized for non-linear and non-sinusoidal systems because they are not able to explain correctly the current and voltage interactions beyond the active power. This paper proposes the use of a novel mathematical framework called geometric algebra (GA) to study the power flow considering the interaction of current and voltage harmonics and interharmonics. The use of GA enables the precise determination of the direction and magnitude of the total and single active power flow for each component, as well as other power elements related to the non-active power due to cross interaction. Moreover, this paper makes a novel contribution to the definition of interharmonics in geometric algebra space that has not been done before. To test the validity of the method, both linear and non-linear circuits are proposed and solved by applying voltages and currents with harmonic and interharmonic components. The results obtained show that power flow can be analyzed under the prism of the principle of energy conservation (PoCoE) in a way that allows a better understanding of the power spectrum due to the interaction of harmonics and interharmonics of voltage and current.

The paper proposes an innovative solution for managing and ensuring high energy efficiency of power supply systems at high non-linear loads. This is realized by maintaining optimal value of reliability indicators and high quality of power supply. The validation is carried out using analyzes and tests of quality of electromagnetic compatibility (EMC) for increased number of powered frequency converters. It has been proven that the effective use and reduction of energy consumption can be achieved thanks to the unique technological features of the employed electrical devices. This enables a normal operation of the system with decreased power and adequate control of energy processes. The problem of predicting power losses under changing conditions in a decentralized electrical network has been solved based on the theory of electromagnetic compatibility. The influence of the mains mode parameters and the indices of instantaneous distortion of current and voltage waveforms caused by the operation of converters on the resonance phenomena in power supply systems were investigated. Recommendations were developed for the selection of proper parameters of compensators for 6-10 kV and 0.4-0.66 kV circuits based on the analysis of the optimization problem when minimizing active power losses. Results of our findings may aid parties involved in designing and maintaining power networks in various applications, such as mines, etc.